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In LTE systems with heterogeneous user mobilities, low-mobility users favor frequency selective scheduling while high-mobility users benefit from frequency diversity scheduling. To benefit both low- and high-mobility users simultaneously, scheduling exploiting frequency selectivity and diversity is desired. To enable the scheduling, low-complexity user mobility classification to distinguish these two types of users is required. In this paper, we first propose a user mobility classification algorithm, which is robust to different channel delay profiles (CDPs), for single-transmit-antenna systems. Then, we extend it to multiple-input multiple-output (MIMO) systems. A low-complexity scheduling algorithm, exploiting both frequency-selectivity and diversity for low- and high-mobility users simultaneously, is also developed. As demonstrated by the simulation results, the proposed user classification algorithm is robust to different CDPs and the proposed scheduling algorithm is effective.